1. Field of the Invention
The invention relates generally to waveguides including bends, more especially but not exclusively to optical waveguides, such as planar waveguides, and to optical devices incorporating waveguides with bends.
2. Description of the Related Art
Planar waveguides are used extensively in optical communications for optical switching, multiplexing and demultiplexing. Many basic optical components and devices, such as modulators, couplers and splitters, incorporate waveguide bends. Moreover, to achieve high density of integration of optical devices on a single chip or substrate, it is often necessary to interconnect the devices with waveguide bends. The size and insertion loss of the waveguide bends ultimately determine the maximum density of devices that can be integrated into an optical circuit of finite size.
It is well known that the field distribution of a fundamental mode in a curved waveguide is different from that in a straight waveguide. The field mismatch between the respective fundamental modes results in transition losses and in excitation of higher-order modes at the junctions between straight and curved waveguides.
In the prior art, one proposed solution to this problem is to offset the curved waveguide at its junction with an adjoining straight (or curved) waveguide, with the offset being towards the centre of curvature of the curved waveguide [1-4]. A number of examples of such prior art offset waveguide structures are now described.
FIG. 1 of the accompanying drawings shows a prior art structure as envisaged by Kitoh et. al. [2] comprising a curved waveguide 10 with a constant radius of curvature ‘r’ coupled to a straight waveguide 20. The centre line 14 of the curved waveguide 10 is laterally offset by a distance ‘d’ from the centre line 16 of the straight waveguide 20, with the offset being towards the centre of curvature of the curved waveguide 10.
FIG. 2 of the accompanying drawings shows an S-shaped waveguide described by Kitoh et. al. [2] which may be considered as a combination of two of the elements shown in FIG. 1. The S-shaped waveguide comprises an input waveguide 24 and an output waveguide 26 that extends parallel to and laterally displaced from the input waveguide 24. The input waveguide 24 is coupled to a first curved waveguide section 28 which is laterally offset from the input waveguide by a distance ‘d’. The first curved waveguide section 28 is further coupled to a second curved waveguide section 30 of opposite curvature. The offset between the first and second curved waveguide sections 28 and 30 is ‘2d’. The second curved waveguide 30 section is further coupled to the output waveguide 26. The offset between the second curved waveguide 30 and the output waveguide 26 is ‘d’. The first and second curved waveguide sections 28 and 30 have the same radius of curvature.
FIG. 3 of the accompanying drawings shows a waveguide directional coupler described by Kitoh et. al. [2]. The waveguide directional coupler has four arms 47. Each arm 47 consists of a first straight section 44 coupled to a first curved section 45 which is further coupled to a second curved section 46 which, in turn, is further coupled to a straight central section. The curved sections 45 and 46 are offset by a distance ‘2d’ to each other. The straight sections 44 and 49 are offset to curved sections 45 and 46 respectively by distances ‘d’. Each curved section 45 and 46 has the same radius of curvature.
Reference [2] describes how the waveguide junction offsets can be dimensioned to minimize transition losses. However, with this transition loss optimization, the offsets distort the optical field as it travels between the straight and curved sections and excite a small amount of radiative modes.
A different approach for optimizing junction offsets is taken in references [3] and [4] which describe how the waveguide junction offsets can be dimensioned to minimize field distortion. However, with this approach the transition losses are higher.
Although the provision of offsets is effective in theory, in practice it is demanding to fabricate waveguides with the proposed offsets, since low dimensional tolerances are needed.